Jahn-Teller effects in metalloporphyrins and other four-fold symmetric systems

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Abstract
The Jahn-Teller (J-T) effect in systems of four-fold symmetry is well known to differ from that in all other point groups with respect to the nature of the J-T active normal modes of vibration. The present report addresses some previously unnoticed features which are of intrinsic importance in recognizing and understanding the unique manifestations of quadrate symmetry in both the static and dynamic Jahn-Teller effects. We first consider the nature of the static J-T potential surfaces when coupling to and strains in two modes, b 1 and b 2, are included in the hamiltonian. The second part of this paper is devoted to an examination of the dynamic J-T effect in four-fold systems. Utilizing both perturbation theory and numerical solution to the Schrödinger equation, we examine the spin-hamiltonian parameters for a metalloporphyrin 3 Eu triplet state and discuss some dynamical processes, including reorientation of the system between minima, spin-lattice relaxation, and the dependences of these phenomena on the nature and magnitude of the off-diagonal terms in the hamiltonian. There emerge from this analysis several signal differences between the Jahn-Teller effect for a doubly degenerate state in four-fold systems and in the more usual cubic or tetrahedral situation.